{"id":"W4385595281","doi":"10.1016/j.ffa.2023.102271","title":"Remarks on Catalan's equation over function fields","year":2023,"lang":"en","type":"article","venue":"Finite Fields and Their Applications","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"Simons Foundation","keywords":"Mathematics; Prime (order theory); Combinatorics; Field (mathematics); Degree (music); Function (biology); Catalan; Finite field; Ring (chemistry); Constant (computer programming); Function field; Pure mathematics; Physics; Humanities","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002162331,0.0009702626,0.001420193,0.002630913,0.00312623,0.003454919,0.002443961,0.003266799,0.01669168],"category_scores_gemma":[0.004192838,0.0003978632,0.001284434,0.001878986,0.006624207,0.009709036,0.003324543,0.00656051,0.002167818],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003188487,"about_ca_system_score_gemma":0.0009131078,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.007206608,"about_ca_topic_score_gemma":0.003568203,"domain_scores_codex":[0.9985805,0.0004483926,0.00008148744,0.000242269,0.0004545161,0.0001928341],"domain_scores_gemma":[0.9977678,0.001324393,0.0001046361,0.0001776157,0.0004646715,0.0001608669],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001485787,0.000008701465,0.00004300201,0.00003781381,0.000003890289,0.00007273832,0.0001959454,0.0001077832,0.00009621807,0.9842021,0.01355701,0.001659929],"study_design_scores_gemma":[0.00001270486,0.00000710329,0.0001936577,0.00002698313,0.000005964873,0.00009693507,0.0001251551,0.0004228839,0.0001352441,0.9497918,0.04916538,0.00001616577],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.03741091,0.01122573,0.03671695,0.2215029,0.02267573,0.0000609538,0.0009550623,0.0003594459,0.6690924],"genre_scores_gemma":[0.6081818,0.01095467,0.01922548,0.05673411,0.02694126,0.0002040643,0.0007779492,0.0003777892,0.2766029],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01669168,"threshold_uncertainty_score":0.05583924,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03516797136844371,"score_gpt":0.2767362607782514,"score_spread":0.2415682894098077,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}